Advertisements
Advertisements
प्रश्न
Find the range of the following functions given by f(x) = |x − 3|
उत्तर
We know |x| are defined for all real values.
And |x – 3| will always be greater than or equal to 0.
i.e., f(x) ≥ 0
Therefore, the range of f = `[0, oo)`
APPEARS IN
संबंधित प्रश्न
Let A = {−2, −1, 0, 1, 2} and f : A → Z be a function defined by f(x) = x2 − 2x − 3. Find:
(a) range of f, i.e. f(A).
If \[f\left( x \right) = x^3 - \frac{1}{x^3}\] , show that
Let f and g be two real functions defined by \[f\left( x \right) = \sqrt{x + 1}\] and \[g\left( x \right) = \sqrt{9 - x^2}\] . Then, describe function:
(iv) \[\frac{f}{g}\]
Let f : [0, ∞) → R and g : R → R be defined by \[f\left( x \right) = \sqrt{x}\] and g(x) = x. Find f + g, f − g, fg and \[\frac{f}{g}\] .
Let f(x) = x2 and g(x) = 2x+ 1 be two real functions. Find (f + g) (x), (f − g) (x), (fg) (x) and \[\left( \frac{f}{g} \right) \left( x \right)\] .
If f(x) = cos [π2]x + cos [−π2] x, where [x] denotes the greatest integer less than or equal to x, then write the value of f(π).
If \[e^{f\left( x \right)} = \frac{10 + x}{10 - x}\] , x ∈ (−10, 10) and \[f\left( x \right) = kf\left( \frac{200 x}{100 + x^2} \right)\] , then k =
The domain of the function \[f\left( x \right) = \sqrt{5 \left| x \right| - x^2 - 6}\] is
If f(x) = `{(x^2 + 3"," x ≤ 2),(5x + 7"," x > 2):},` then find f(0)
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify.
{(1, 2), (2, −1), (3, 1), (4, 3)}
Find x, if f(x) = g(x) where f(x) = `sqrt(x) - 3`, g(x) = 5 – x
Check the injectivity and surjectivity of the following function.
f : N → N given by f(x) = x2
Express the following exponential equation in logarithmic form
54° = 1
Express the following exponential equation in logarithmic form
`9^(3/2)` = 27
Express the following exponential equation in logarithmic form
e2 = 7.3890
Select the correct answer from given alternatives.
Find x, if 2log2 x = 4
Select the correct answer from given alternatives
If f(x) = 2x2 + bx + c and f(0) = 3 and f(2) = 1, then f(1) is equal to
Answer the following:
Find whether the following function is one-one
f : R → R defined by f(x) = x2 + 5
Answer the following:
If b2 = ac. prove that, log a + log c = 2 log b
Answer the following:
If `log_2"a"/4 = log_2"b"/6 = log_2"c"/(3"k")` and a3b2c = 1 find the value of k
Answer the following:
Find the domain of the following function.
f(x) = 5–xPx–1
Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x2 + 1} is a function from X to N?
Find the domain of the following function.
f(x) = `x/(x^2 + 3x + 2)`
Find the range of the following functions given by `sqrt(16 - x^2)`
The domain for which the functions defined by f(x) = 3x2 – 1 and g(x) = 3 + x are equal is ______.
Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If f(g(x)) = 8x2 – 2x, and g(f(x)) = 4x2 + 6x + 1, then the value of f(2) + g(2) is ______.
Let f(θ) = sin θ (sin θ + sin 3θ) then ______.
